In this article, I briefly present an experimental lesson – from Descartes ’ multiplication to the geometric meaning of the product of complex numbers – connecting multiplication and some of its geometric meanings. I will also present some examples of our experiments conducted in French high schools and some elements of the analysis process to identify the possibilities of connecting multiplication and some of its geometric meanings through the production of interactions between different registers of representation and a semiotic mediation within a Mathematical Work Space (MWS). « For every question and every phenomenon, in order to follow the normal psychological route of scientific thought, we must go from an image to a geometric figure, and then from a geometric figure to an abstract form. » (Translation, Bachelard, 1938, p. 10.) Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York
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